Final answer:
The end behavior of a graph is determined by the leading term of the function. If the leading term is positive, y approaches positive infinity as x approaches positive infinity. If the leading term is negative, y approaches negative infinity. In this case, the graph has a positive leading coefficient for positive infinity and a negative leading coefficient for negative infinity.
Step-by-step explanation:
The end behavior of a graph describes what happens to the values of y as x becomes extremely large (approaches positive infinity) or extremely small (approaches negative infinity). To determine the end behavior of a graph, we look at the leading term of the function. If the leading term is positive, as x approaches positive infinity, y will also approach positive infinity. If the leading term is negative, as x approaches positive infinity, y will approach negative infinity. Similarly, as x approaches negative infinity, the behavior of y will depend on the leading coefficient. If the leading coefficient is positive, y will approach positive infinity. If the leading coefficient is negative, y will approach negative infinity.
In this case, we are given that as x approaches positive infinity, y approaches a.[infinity]. This indicates that the leading coefficient is positive. And as x approaches negative infinity, y approaches b.[negative infinity]. This suggests that the leading coefficient is negative.